A. Yellow Cards ( Codeforces Round #585 (Div. 2) 思维水题

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output

standard output

The final match of the Berland Football Cup has been held recently. The referee has shown n yellow cards throughout the match. At the beginning of the match there were a_1 players in the first team and a_2 players in the second team.

The rules of sending players off the game are a bit different in Berland football. If a player from the first team receives k_1 yellow cards throughout the match, he can no longer participate in the match — he's sent off. And if a player from the second team receives k_2 yellow cards, he's sent off. After a player leaves the match, he can no longer receive any yellow cards. Each of n yellow cards was shown to exactly one player. Even if all players from one team (or even from both teams) leave the match, the game still continues.

The referee has lost his records on who has received each yellow card. Help him to determine the minimum and the maximum number of players that could have been thrown out of the game.

Input

The first line contains one integer a_1 (1 le a_1 le 1\,000) — the number of players in the first team.

The second line contains one integer a_2 (1 le a_2 le 1\,000) — the number of players in the second team.

The third line contains one integer k_1 (1 le k_1 le 1\,000) — the maximum number of yellow cards a player from the first team can receive (after receiving that many yellow cards, he leaves the game).

The fourth line contains one integer k_2 (1 le k_2 le 1\,000) — the maximum number of yellow cards a player from the second team can receive (after receiving that many yellow cards, he leaves the game).

The fifth line contains one integer n (1 le n le a_1 cdot k_1 + a_2 cdot k_2) — the number of yellow cards that have been shown during the match.

Output

Print two integers — the minimum and the maximum number of players that could have been thrown out of the game.

Examples

input

Copy

2
3
5
1
8

output

Copy

0 4

input

Copy

3
1
6
7
25

output

Copy

4 4

input

Copy

6
4
9
10
89

output

Copy

5 9

Note

In the first example it could be possible that no player left the game, so the first number in the output is 0. The maximum possible number of players that could have been forced to leave the game is 4 — one player from the first team, and three players from the second.

In the second example the maximum possible number of yellow cards has been shown (3 cdot 6 + 1 cdot 7 = 25), so in any case all players were sent off.

地址：http://codeforces.com/contest/1215/problem/A

　　　　题意：

　　　　　　　　

　　　　　　对于最少的情况：两队分别是k1，k2张，那么让每个人得k1-1,k2-1张。一共为 m==a1*(k1-1)+a2*(k2-1);　这个m就是，如果n>m,就可以有人下场，n<=m，用贪心思想，可以做到无人下场。n>m的时候，由于k1-1,k2-1的原因，每个人只需要1票就下场了。让每个人都得到了k1-1,k2-1的票数，那么n每比m多一个，就一个人下场所以此时n-m即为最少下场人数。

　　　　　　对于最大的情况：我习惯用k1<k2，所以做了swap的处理。

　　　　　　　　　　　　　　求最大，肯定从需票数少的一队入手。a2*k2如果大于等于n，那么直接就是max==n/k2;否则，n=n-n/k2;用这个余下的n去比上k1即可了。

　　　　　　主要是思想，最少的情况里，根据贪心思想，要想一个人不退场，那么我的总票数不能大于  a1*(k1-1)+a2*(k2-1),如果大于了，这个操作使每个人只需一票就要下场了，n-就可以了。

　　　　上代码：

　　　　

#include<iostream>
#include<cstdio>
using namespace std;
int main()
{
    int a1,a2,k1,k2,n;
    cin>>a1>>a2>>k1>>k2>>n;
    int minn,maxx=0;
    int k=a1*(k1-1)+a2*(k2-1);
    if(n<=k)
        minn=0;
    else
        {
            minn=n-k;
        }
    if(k1<k2)
    {
        swap(k1,k2);
        swap(a1,a2);
    }
//    cout<<a2<<" "<<k2<<endl;
    if(a2*k2<n)
    {
        maxx+=a2;
        n-=a2*k2;
        maxx+=n/k1;
    
    }
    else
    {
        maxx+=n/k2;
    }
    cout<<minn<<' '<<maxx<<endl;
}